Wavelet extraction method based on fractional number order Fourier
Technical field
The present invention relates to the seismic exploration technique field.More particularly, relate to a kind of wavelet extraction method based on fractional order Fourier (FRFT) territory of in seismic prospecting, using.
Background technology
Seismic exploration technique is gradually to high precision, high resolving power future development, and accurately extracting wavelet is the basis of deconvolution, wave impedance inversion and forward simulation.Nearly twenty or thirty year, people have proposed the algorithm of a lot of wavelet extractions, and obtained certain effect, but existing methods of seismic wavelet extraction all has deficiency separately, and the wavelet precision of extracting is not high, affects one of further key factor that improves of seismic inversion so that the wavelet extraction technology becomes.Conventional algorithm supposes that all the stratum is a time-invariant system, yet, owing to the variation of subsurface formations information along with the degree of depth changes, therefore it is a time-varying system, so describing it with linear time invariant system must be not accurate enough, thereby cause the wavelet extraction precision relatively poor, wave impedance inversion result and drilling geology are misfitted, the reservoir prediction difficulty.Therefore, seek a kind of method, with time-varying system subsurface formations information is described, remedy conventional Fourier can not process when non-become, the deficiency of non-stationary process, improve the precision of wavelet extraction, improve and carry out the accuracy of seismic layer labeling and the resolution of seismic inversion, carry out more accurately bonding layer prediction and fluid identification.
The extracting method of seismic wavelet comprises two large classes at present, and the first kind is that determinacy is extracted wavelet, and Equations of The Second Kind is that statistical is extracted wavelet.The first kind refers to suppose that reflection coefficient can have well logging to calculate, and in conjunction with seismic trace near well, obtains seismic wavelet by convolution theory, namely seismologic record is regarded as the convolution of wavelet and reflection coefficient.Equations of The Second Kind is that the hypothesis seismic wavelet is constant when being, underground reflection coefficient sequence has the white noise random series, does not need to calculate reflection coefficient sequence, and according to the statistical information (second-order statistic, high-order statistic) of seismic trace, estimates seismic wavelet.Common wavelet extraction method has:
(1) auto-correlation algorithm
The method is extracted seismic wavelet based on second-order statistic (autocorrelation function) method, at first proposed by Robinson (1975), suppose when seismic wavelet is constant, underground reflectivity is the random series with white noise spectrum, these hypothesis mean that the spectral amplitude of geological data and the spectral amplitude of seismic wavelet only differ a constant, namely can be in the hope of the spectral amplitude of seismic wavelet, phase spectrum for wavelet, then must provide some hypothesis (minimum phases, zero phase or maximum phase), can try to achieve wavelet by the Fourier transform of negating again, but the method can not be extracted the phase information of wavelet.
(2) homomorphism method
The method basic thought is that convolution signal is carried out Fourier transform, gets the product of two signals, take the logarithm again be two signals and, namely the nonlinear properties in the time domain are converted to linear signal in the frequency domain, in frequency domain, it is separated.It is the logarithm of its Fourier transform that the intermediary heat of a critical sequences is composed.Supposed that seismic wavelet is metastable, its corresponding intermediary heat spectrum also is approximate constant, and the stratum reflection coefficient thinks that it is random variation, and corresponding intermediary heat spectrum is to change.When carrying out the multiple tracks stack, because the seismic wavelet on the per pass all is similar to stable, thus when stack, obtained reinforcement, and reflection coefficient changes, what just may be similar to when stack balances out, thereby the cepstrum of whole seismic model has just become the intermediary heat spectrum of seismic wavelet.The method is very sensitive to noise, and the effect of the lower geological data of signal to noise ratio (S/N ratio) being extracted wavelet is relatively poor.
(3) Roy White wavelet extraction method
The method is that a kind of the employing demarcated and made well data and geological data is interrelated obtains earthquake from the method for wavelet optimal estimation, belongs to the determinate wavelet pickup method, and it does not need to suppose the phase place of wavelet.Ideally, this algorithm in two steps: the optimum position of determining to extract the used well of wavelet; Determine best wavelet in this position.Its supposition drilling well position relevant with geological data may not be the ideal position of extraction wavelet, and the seismic sweep algorithm can find new position effectively near the fixed well position.Because this algorithm is used log data, so it is very large to the precision dependence of log data to extract the precision of wavelet.
(4) Higher order Statistics
High-order statistic (higher-order spectrum) is compared with second-order statistic (power spectrum), except the abundanter quantity of information (such as complete phase information) that comprises signal, also has any Gaussian noise signal characteristic blindly, can in the coloured Gaussian noise under any intensity, extract the phase information of non-Gaussian signal, broken away from some hypothesis of sub-wave phase and additive noise, this has solved the problem that other method of a lot of usefulness cann't be solved.The shortcoming of this algorithm is that calculated amount is very large.
Summary of the invention
The present invention uses time-varying system (Fourier Transform of Fractional Order FrFT) to describe formation information, the true medium situation of more realistic stratum geological system, can improve the precision of seismic wavelet extraction, further improve resolution and the precision of seismic inversion, reservoir prediction.Method of the present invention utilizes the FrFT second-order cumulant of seismologic record, log data to extract seismic wavelet, has avoided using calculating numerous and diverse, and the Higher-order Cumulants that operand is huge extracts seismic wavelet.
According to an aspect of the present invention, provide a kind of wavelet extraction method based on fractional number order Fourier, having comprised: set up the formation information initial model; Utilize the reflection coefficient theogram of input wavelet and formation information initial model; Calculate input wavelet and the cross-correlation matrix of the seismologic record data of synthesizing and the autocorrelation matrix of seismologic record data, and described cross-correlation matrix and autocorrelation matrix are carried out Fourier Transform of Fractional Order; The optimal filtering algorithm of described cross-correlation matrix and autocorrelation matrix application fractional number order Fourier is calculated optimal order and the optimal filtering operator of square error minimum; Extract wavelet based on described optimal filtering operator and optimal order, wherein, optimum operator f (m) is represented by following equation:
Wherein,
With
The Fourier Transform of Fractional Order that represents respectively described cross-correlation matrix and autocorrelation matrix, and extract wavelet by following equation
Wherein, y represents the column vector of the sample sequence of seismic signal, y=Hx+n, and p represents optimal order;
Wherein, x is the column vector of the sample sequence of expression input wavelet, and n represents the column vector of the sample sequence of noise, and H represents the reflection coefficient matrix.
According to an aspect of the present invention, described wavelet extraction method also comprises: the wavelet extracted and original input wavelet are compared.
The formation information initial model that becomes when according to an aspect of the present invention, described formation information initial model is.
According to an aspect of the present invention, described input wavelet is the true wavelet of extracting in theoretical wavelet or actual seismic data and the well-log information.
According to an aspect of the present invention, search optimal order p in the scope of (2,2).
Description of drawings
By the description of carrying out below in conjunction with accompanying drawing, above and other purpose of the present invention and characteristics will become apparent, wherein:
Fig. 1 is the process flow diagram that illustrates according to the wavelet extraction method based on the FRFT territory of the present invention;
Fig. 2 is the schematic diagram that illustrates according to the original input wavelet of the embodiment of the invention;
Fig. 3 illustrates the input wavelet by synthetic after the time-varying system, the schematic diagram of the seismologic record of plus noise not;
Fig. 4 is the schematic diagram that is illustrated in the wavelet that traditional Fourier extracts the theogram of plus noise not;
Fig. 5 illustrates the schematic diagram that uses according to the wavelet of the theogram of plus noise not being extracted based on the wavelet extraction method in FRFT territory of the embodiment of the invention;
Fig. 6 be illustrate the input wavelet by time-varying system after the schematic diagram of seismologic record synthetic, that be added with Gaussian noise;
Fig. 7 is the schematic diagram that is illustrated in the wavelet that traditional Fourier extracts the theogram of having added noise;
Fig. 8 illustrates the schematic diagram that uses according to the wavelet of the theogram of having added noise being extracted based on the wavelet extraction method in FRFT territory of the embodiment of the invention;
Fig. 9 illustrates the schematic diagram that uses according to the wavelet of the theogram of the Gaussian noise of having added different signal to noise ratio (S/N ratio)s being extracted based on the wavelet extraction method in FRFT territory of the embodiment of the invention.
Embodiment
The below provides the description carried out with reference to accompanying drawing to help complete understanding such as claim and exemplary embodiment of the present invention that equivalent was limited thereof.Described description comprises that various detailed details understand helping, and these descriptions will be considered to only for exemplary.Therefore, those of ordinary skill in the art will recognize in the situation that do not depart from the scope of the present invention with spirit and can make various change described here and modification.In addition, for clear and succinct, can omit the description to known function and structure.
Fig. 1 is the process flow diagram that illustrates according to the wavelet extraction method based on the FRFT territory of the present invention.
At first, at step S101, set up the formation information initial model.This formation information initial model is for generation of the seismologic record reflection coefficient.Preferably, according to the present invention, the stratum initial model that becomes in the time of can setting up.The benefit of the formation information initial model that becomes during employing is the truth of more realistic stratum system.According to one embodiment of present invention, the formation information initial model that becomes in the time of can adopting following equation to simulate such as the linear time varying system of expression:
h(t,t′)=exp(-j2πt(t-t′))sinc(t-t′) (1)
Should be understood that the formation information initial model that becomes when above only is an example, also can adopt other time-varying system to make up the formation information initial model.
Next, at step S102, utilize the reflection coefficient theogram of input wavelet and formation information initial model.According to one embodiment of present invention, the input wavelet can be theoretical wavelet, for example, and Ricker wavelet as shown in Figure 2.According to another embodiment of the present invention, the input wavelet can be the true wavelet of extracting in actual seismic data and the well-log information.
Then, at step S103, calculate the correlation matrix of input wavelet and the seismologic record data of synthesizing, and correlation matrix is carried out p rank fractional fourier transform.Particularly, usually, the observation model of seismic signal can be represented by following equation (2):
y=Hx+n (2)
Wherein, y is that column vector, the x of the sample sequence of expression seismic signal is the column vector of the sample sequence of expression input wavelet, and n represents the column vector of the sample sequence of noise, and H represents the reflection coefficient matrix.Calculate the cross-correlation matrix Rxy=E[xy of input wavelet and seismologic record data
H] and the autocorrelation matrix Ryy=E[yy of seismologic record data
H].The autocorrelation matrix of supposing input wavelet and noise is respectively R
XxAnd R
Nn, correlation matrix R then
YyAnd R
XyP rank fractional fourier transform can be expressed as respectively following equation (3) and (4):
Next, at step S104, the correlation matrix based on input wavelet and the seismologic record data of synthesizing utilizes the optimal filtering algorithm of fractional number order Fourier to calculate the optimal order that makes the square error minimum, and calculates optimal filtering operator f (m).Particularly, can pass through the p value is searched for to calculate the optimal order of square error minimum in the scope of (2,2), and can calculate optimum operator f (m) by following equation (5):
Then, at step S105, extract wavelet based on optimal order and optimum operator.Can calculate wavelet by equation (6)
At last, can also show the wavelet of extracting at step S106, thereby the wavelet of extraction and original input wavelet are compared analysis.
Fig. 2-Fig. 9 shows respectively the input wavelet of plus noise not and has added the synthetic seismologic record of the input wavelet of noise, input wavelet and the schematic diagram of the wavelet extracted according to traditional Fourier with according to FRFT of the present invention territory respectively.Wherein, Fig. 3 illustrates the input wavelet by synthetic after the time-varying system, the schematic diagram of the seismologic record of plus noise not; Fig. 4 is the schematic diagram that is illustrated in the wavelet that traditional Fourier extracts the theogram of plus noise not; Fig. 5 illustrates the schematic diagram that uses according to the wavelet of the theogram of plus noise not being extracted based on the wavelet extraction method in FRFT territory of the embodiment of the invention; Fig. 6 be illustrate the input wavelet by time-varying system after the schematic diagram of seismologic record synthetic, that be added with Gaussian noise; Fig. 7 is the schematic diagram that is illustrated in the wavelet that traditional Fourier extracts the theogram of having added noise; Fig. 8 illustrates the schematic diagram that uses according to the wavelet of the theogram of having added noise being extracted based on the wavelet extraction method in FRFT territory of the embodiment of the invention; Fig. 9 illustrates the schematic diagram that uses according to the wavelet of the theogram of the Gaussian noise of having added different signal to noise ratio (S/N ratio)s being extracted based on the wavelet extraction method in FRFT territory of the embodiment of the invention.
Contrast by above accompanying drawing can be found out, no matter be at plus noise or not in the plus noise seismologic record according to the wavelet extraction method based on the FRFT territory of the present invention, can both more intactly extract the Main Morphology of original wavelet, and the effect of extraction wavelet is all effective than conventional Fourier transform method.Especially, in Fig. 9, added the Gaussian noise of different signal to noise ratio (S/N ratio)s after, can more intactly extract the Main Morphology of original wavelet according to wavelet extraction method of the present invention, have certain anti-noise ability.
Wavelet extraction method according to the present invention can be recorded in and comprise in the computer-readable medium of execution by the programmed instruction of computer implemented various operations.Medium also can include only programmed instruction or comprise the data file that combines with programmed instruction, data structure etc.The example of computer-readable medium comprises magnetic medium (for example hard disk, floppy disk and tape); Optical medium (for example CD-ROM and DVD); Magnet-optical medium (for example, CD); And special preparation is used for the hardware unit (for example, ROM (read-only memory) (ROM), random access memory (RAM), flash memory etc.) of storage and execution of program instructions.Medium also can be the transmission medium (such as optical line or metal wire, waveguide etc.) that comprises the carrier wave of the signal that transmits established procedure instruction, data structure etc.The example of programmed instruction for example comprises the machine code that is produced by compiler and comprises the file that can use the high-level code that interpreter carried out by computing machine.
Although specifically shown with reference to exemplary embodiment of the present invention and described the present invention, but it should be appreciated by those skilled in the art, in the situation that does not break away from the spirit and scope of the present invention that are defined by the claims, can carry out various changes on form and the details to it.